Mean Proportional

Means and Extremes In a proportion, the product of the means is equal to the product of the extremes Means Extremes

Mean Proportional If the two means of the proportional are equal , it is called the mean proportional between the first and fourth terms. In the proportion the mean proportional is? The mean proportional is also known as the geometric mean

Mean Proportional Page 38 Which of the following represents the geometric mean of 4 and 9? (1) 6 (3) 18 (2) 6.5 (4) 36 4 𝑥 = 𝑥 9 𝑥=±6 𝑥=6 𝑥 2 =36 𝑥 2 = 36 3. 8 is the geometric mean between 4 and which of the following values? (1) 64 (3) 16 (2) 24 (4) 4 4 8 = 8 𝑥 4𝑥 4 = 64 4 4𝑥=64 𝑥=16

Page 39 Theorems Right Triangle Altitude Theorem – If the altitude of a right triangle is drawn (to the hypotenuse), then it divides the triangle into two similar triangles that are similar to the original. A C D B

Start by filling in the mean proportional Page 39 Theorems Mean proportionality theorem – The altitude of a right triangle is the mean proportional between the segments into which it divides the hypotenuse. Start by filling in the mean proportional Altitude Mean Propotional A Lets try with some values Solve for x! 9 C x D 27 B Two parts of the hypotenuse

Page 39 Notice that we did not have the ± in front of our answer this time. Why? 6 𝑥 = 𝑥 3 𝑥= 9∙2 𝑥=3 2 𝑥 2 =18 𝑥 2 = 18

4 𝑥 = 𝑥 9 𝑥 2 =36 𝑥 2 = 36 𝑥=6

Page 40 18 𝑥+9 = 𝑥+9 8 𝑥+9 𝑥+9 =144 𝑥 2 +9𝑥+9𝑥+81=144 𝑥 2 +18𝑥+81=144 −144−144 𝑥 2 +18𝑥−63=0 𝑥+21 𝑥−3 =0 𝑥+21=0 𝑥−3=0 𝑥=−21 𝑥=3 REJECT

Page 43 9 12 = 12 𝑥 12 9𝑥=144 9𝑥 9 = 144 9 9 𝑥 𝑥=16

Page 43 4 8 = 8 𝑥 8 4𝑥=64 4𝑥 4 = 64 4 4 𝑥 𝑥=16

Homework Page 43 #11,15,17,21,22,23 Separate Sheet

Page 43 3 6 = 6 𝑥 6 3𝑥=36 3𝑥 3 = 36 3 3 𝑥 𝑥=12

Page 43 4 𝑥 = 𝑥 9 𝑥 𝑥 2 =36 𝑥 2 = 36 4 9 𝑥=6

Page 43 3 𝑥 = 𝑥 27 𝑥 𝑥 2 =81 𝑥 2 = 81 3 27 𝑥=9

Page 43 5 𝑥 = 𝑥 20 𝑥 2 =100 𝑥 𝑥 2 = 100 𝑥=10 5 20

Page 43 2 8 = 8 𝑥 8 2𝑥=64 2𝑥 2 = 64 2 2 𝑥 𝑥=32

Page 43 𝑥 6 = 6 9𝑥 9𝑥 2 =36 6 9𝑥 2 9 = 36 9 𝑥 2 =4 𝑥 9𝑥 𝑥 2 = 4 𝑥=2 9𝑥=2∙9=18 𝑥=2